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1. What is the remainder when 41000 is divisible by 7 By simplest and elaborative method so that a 10th class student can understand.

If in ΔABC, ∠C = 90°. Then, the value of cos(A + B) is



(a) 0



(b) 1



(c) $\frac{1}{2}$



(d) $\frac{3}{5}$

In the ___ method of calculating mean we divide the deviations by the same number to simplify calculations.

A solid wooden toy is in the shape of a right circular cone mounted on a hemisphere. If the radius of the hemisphere is 4.2 cm and the total height of the toy is 10.2 cm, find the volume of the wooden toy. [4 MARKS]

(i) For which values of a and b will the following pair of linear equations have an

infinite number of solutions?

(ii) For which value of k will the following pair of linear equations have no solution?

The radii of two circles are 19 cm and 9 cm respectively. The radius of the circle which has its circumference equal to the sum of the circumferences of the two circles is:

If $sec\Theta +tan\Theta =p$. Show that $\frac{p^2-1}{p^2+1}=sin\Theta$

The system of pair of equations $4x-3y+12=0$ and $2x+3y-15=0$ has

What is the function of the underlined modals in the sentences?

The mean proportional of the line segments of length 3 cm and 6 cm is ___ (Use geometric method).

Chaman maintains his books according to Single Entry System. Following figures were available from the books for the six months ended 31st December 2018:

Adjustments:

(a) He had withdrawn ₹ 200 in the beginning of every month for household purposes.

(b) Depreciation on Plant and Machinery 10% p.a.

(c) Further Bad Debts ₹ 5,000 and Provision for Doubtful Debts to be created 2%.

(d) During the period, salaries have been prepaid by ₹ 500 while wages outstanding were ₹ 1,000.

(e) Interest on drawings to be reckoned 6% p.a.

You are required to prepare the Statement of Profit or Loss for the half year ended 31st December, 2018, followed by Revised Statement of Affairs as on that date.

If $\tan \left(\frac{\pi }{8}\right)$ is a root of the equation $x^2+ax+b=0,$ where $a$ and $b$ are rational numbers, then the value of $a^2+b^2$ is

Question 3

In a right circular cone, height, radius and slant height need not always to be the sides of a right triangle.

The polynomial with $1,\frac{1}{2}\&\frac{-1}{2}$ as zeroes is ______

A train covered a certain distance at a uniform speed. If the train could have been 10 km/hr. faster, it would have taken 2 hours less than the scheduled time. And,if the train were slower by 10 km/hr;if would have taken 3 hours more than the scheduled time. Find the distance covered by the train.

Construct a cyclic quadrilateral EFGH with EF = 6 cm,$\angle GEF={60}^{\circ }$, FG = 7cm and $\angle EGH={50}^{\circ }$.

39 students were asked about the number of people in their families.

The table shows the results. From the table, estimate the median.

$\begin{array}{cc}\text{Number of people in the family}& \text{frequency}\\ 2& 1\\ 3& 1\\ 4& 17\\ 5& 12\\ 6& 6\\ 7& 2\end{array}$

Find the sum of all odd numbers between 0 and 50.

105 goats, 140 donkeys and 175 cows have to be taken across a river. There is only one boat which will have to make many trips in order to do so. The lazy boatman has his own conditions for transporting them. He insists that he will take the same number of animals in every trip and they have to be of the same kind. He will naturally like to take the largest possible number each time. Can you tell how many animals went in each trip?

Check the validity
of the statements given below by the method given against it.

(i) p:
The sum of an irrational number and a rational number is irrational
(by contradiction method).

(ii) q:
If n
is a real number with n
> 3, then n²
> 9 (by contradiction method).

If two vertices of a parallelogram are (3, 2), (-1, 0) and the diagonals cut at (2, -5), find the remaining two vertices of the parallelogram.

Evaluate the following:
$2sin{30}^{\circ }+3cos{60}^{\circ }–3tan{45}^{\circ }$

In the following figure, A, B and C are points on OP, OQ and OR respectively such that AB || PQ and AC || PR. Show that BC || QR.

Find $a_{20}$ of a geometric sequence, if the first few terms of the sequence are given by $-\frac{1}{2},\frac{1}{4},-\frac{1}{8},\frac{1}{16},\cdots$

The value of sec0${}^{\circ }$ = y

If secx and tanx are not defined at some x < 100${}^{\circ }$ , then x + y = __

The following table shows the weights of $12$ workers in a factory:

$\begin{array}{cccccc}\text{Weight (in kg)}& 60& 63& 66& 69& 72\\ \text{No. of workers}& 4& 3& 2& 2& 1\end{array}$

Find the mean weight of the workers.

In the figure above, DE and CE are the tangents through the point E. AF and AB are the tangents through the point F to the circle with centre M.

Also, $\angle DEM={30}^{\circ }$ and $\angle AFM={10}^{\circ }$

What is the value of $\angle MFB+\angle MEC=?$

Question 7
How many solution(s) of the equation 2x + 1 = x - 3 are there on the:
(i) number line?
(ii) Cartesian plane?

Question 8

Pictorial representation of $3\times \frac{2}{3}$ is

Draw an equilateral triangle of sides 6 centimetres and draw its incircle and circumcircle.

Question 7

Which constant must be added and subtracted to solve the quadratic equation $9x^2+\frac{3}{4}x-\sqrt{2}=0$ by the method of completing the square?

(A) $\frac{1}{8}$

(B) $\frac{1}{64}$

(C) $\frac{1}{4}$

(D) $\frac{9}{64}$

In the given figure if $\angle GHE=\angle DFE={90}^{\circ }$, DH = 8 cm, DF = 12 cm, DG = 3x - 1 and DE = 4x + 2, then DG and DE are respectively ___.